Analytical solution of rotationally symmetric Stokes flow near corners. (English) Zbl 1340.76025

Burda, Pavel; Novotný, Jaroslav; Šístek, Jakub

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 15–17, 2013. In honor of the 70th birthday of Karel Segeth. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-61-5). 13-20 (2013).

An analytical solution of the Stokes problem in 2D domains is presented, which is then used to characterize the singular part of the solution of the Stokes and Navier-Stokes equations near corners on the boundary of the domain. This approach leads to a very precise numerical finite element solution, which is also illustrated on two numerical examples: flow in a channel with forward and backward steps and a lid driven cavity.
For the entire collection see [Zbl 1277.00032].

Reviewer: Marta Čertíková (Praha)

MSC:

76D07	Stokes and related (Oseen, etc.) flows
76D05	Navier-Stokes equations for incompressible viscous fluids
76M10	Finite element methods applied to problems in fluid mechanics
76M45	Asymptotic methods, singular perturbations applied to problems in fluid mechanics

Keywords:

Stokes flow; Navier-Stokes equations; asymptotic behaviour; singularity; boundary corner; finite element method; flow in a channel; lid driven cavity

Software:

Gmsh